Submitted by, APOORVA PRAKASH H S(1SI09EC118)

Under the guidance of,Dr. K.V. Suresh, M.Tech, Ph.D.,Professor and HeadDepartment of E&CSIT, Tumkur

Image denoising in the wavelet domain using Wiener filtering

DEPARTMENT OF ELECTRONICS AND COMMUNICATION, 2012-2013

Technical Seminar on

Outline

IntroductionLocal Wiener filteringDoubly local Wiener filteringExperimental resultsConclusionReferences

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Why do we want to denoise

Visually unpleasantBad for compressionBad for analysis

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Introduction

Image denoising means removing unwanted noise in order to restore the original image

Wavelet transform provides us with one of the best methods for image denoising

Squared window

Elliptical directional window to improve further denoising performance

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Problem statementY = X + W

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= +

Y: Noisy image X: Original image W: White Gaussian noise

Assumptions • X is unknown• X and W are uncorrelated• Noise variance may be unknown

Goal: recover X from Y

Noise removal techniques

Linear filteringNon linear filtering Recall

H[ai fi(x) +aj fj(x) = ai H[fi(x)] + aj H[fj(x)]

= ai gi(x) +aj gj(x)

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SystemH

f(x) g(x)

Local Wiener filtering

1) Original Barbara image2) Horizontal subband3) Vertical subband4) Diagonal subband

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1 2 3 4

Figure 1: Three undecimated oriented subbands in the third level for the image “Barbara” [3]

Local Wiener filtering(contd.)

A longer elliptic window is used for horizontal subband

A higher elliptic window is used for vertical subband

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(1)

Local Wiener filtering(contd.)

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The local wiener filtering in the wavelet domain includes two important steps;

• Signal variance estimation

• Signal wavelet coefficient estimation

(2)

Local Wiener filtering(contd.)

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The signal variance of each noisy wavelet coefficient is estimated by the local average

The signal wavelet coefficients are estimated by the Wiener filtering

(3)

(4)

Doubly local Weiner filtering

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Figure 2: Flow diagram of the DLWFDW in the wavelet domain [3]

Doubly local Weiner filtering(contd.)

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The total error in each subband is written as

Selecting a too large or too small window is not a good choice

(5)

Primary guides about size selection

For the decimated case, the optimal sizes of the windows that minimize the total error should be gradually reduced

For the undecimated case, the optimal sizes of the windows should be gradually increased with scales

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How to select wavelet pairs

In the first LWFDW, wavelet bases of short support are often used as the DWT1 or SWT1

In the second LWFDW, wavelet bases of high vanishing moments are often used as the DWT2 or SWT2

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Experimental results

σ 10 15 20 25

D3+D4 33.05 30.66 29.07 27.86

D4+S8 33.24 30.85 29.27 28.07

D3+S8 33.16 30.81 29.26 28.08

S8+S8 33.02 30.71 29.16 28.01

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Table 1: comparison of different wavelet pairs [3]

Experimental results(contd.)

r 5 6 7 8 9

a=1 31.61 31.99 32.07 32.10 32.07

a=2 32.03 32.15 32.20 32.19 32.15

a=3 32.10 32.19 32.19 32.13 32.08

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Table 2: comparison of different windows [3]

Conclusion

Doubly Local Wiener Filtering algorithm is an efficient, fast approach and low complexity

The algorithm outperforms the relevant algorithms using the 2-D separable wavelets

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References[1] M. K. Mihcak, I. Kozinsev, K. Ramchandran, and P.

Moulin, “Low-complexity image denoising based on statistical modeling of wavelet coefficients,” IEEE Signal Process. Lett., vol. 7, no. 6, pp. 300–303, Jun. 1999.

 [2] S.P.Ghael, A.M.Sayeed and R.G.Baraniuk,

“Improved wavelet denoising via empirical Wiener filtering” in Proc. SPIE, vol. V, San Diego, CA, pp. 389–399, July 1997. 

[3] Peng-Lang shui, “Image denoising algorithm via doubly local wiener filtering” Lett., vol. 12, no. 10, pp. 681-684, Oct 2005

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Thank you

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